Find the following limits. Try to use L'Hospital if possible.

Question

a) lim as x approaches infinity of (2^x+1)/(3^x+1)

I got type infinity/infinity so I started by finding f'(x)/g'(x) and writing a^x as e^xlna. But I don't think this was correct.

b) lim as x approaches 0 from the right of (lnx-lnsinx)

c) lim as x approaches 0 from the right of (1+1/x)^x

Would I use the exponential types to use L'H?

Answer 1

a) lim as x approaches infinity of (2^x+1)/(3^x+1)=0

b) lim as x approaches 0 from the right of (lnx-lnsinx)=0

c) lim as x approaches 0 from the right of (1+1/x)^x =1